National data in the 1960s showed that about 44% of the adult population had never smoked cigarettes. More recently, a national health survey interviewed a random sample of 881 adults and found that 47.1% had never been smokers. (using the R code (Rstidio) to answer the questions) Does the recent data provide evidence of a change in behavior for the better among Americans? a) State the null and alternative hypotheses. Define the parameter in the context of the problem. b) Assume the null hypothesis is true. Describe the sampling distribution of the statistic. Shape: Mean: Standard Deviation: c) If the null hypothesis is true, what two values would capture the middle 99% of all sample proportions? Is the proportion based on the data within this range? d) Is it reasonable to conclude the responses of the 881 adults are independent? e) What is the probability of obtaining a sample as extreme as the one obtained? At the 0.01 level of significance, is this enough evidence to conclude the proportion that have never smoked has changed since the 1960s? Explain